Shut-off valves are shut-off devices widely used in water resources engineering. They are frequently designed as butterfly valves with a flap- or disk-shaped valve body, which is pivotably mounted about an axis of rotation inside a shut-off valve housing and which can be swiveled between a closed position and an open position. As a rule, the shut-off valve housings of this type of shut-off devices comprise a main body made of metal and having a valve seat disposed inside a through-channel of the main body, against which valve seat the flap-or disk-shaped valve body, when in the closed position, rests by way of a gasket. To keep the flow losses in the shut-off valves in the open position as low as possible, the valve body, as well as the through-channel of the associated shut-off valve housing, should be designed so as to promote the flow of the fluid as efficiently as possible. Calculations have shown that the fluid flow promoting design of the valve seat has a significant influence on the flow resistance of the shut-off valve. To ensure that the medium flowing through the through-channel in the open position of the shut-off valve is able to impinge on the housing wall of the shut-off valve housing with the lowest possible flow resistance after having passed the flow-inhibiting and medium-accelerating valve seat, the through-channel in the prior-art shut-off valve housings in many cases undergoes a conical or abrupt expansion of the cross section on the outflow side of the valve seat. However, from the standpoint of fluid technology, this type of through-channel design leaves much to be desired.